Question

In the following exercises, add or subtract.

$\frac{10v}{2v-1}+\frac{2v+4}{1-2v}$

Short answer

The sum of both the expressions is 4.

Step-by-step solution

Step 1. Given Information

The given expression is$\frac{10v}{2v-1}+\frac{2v+4}{1-2v}$.

Step 2. Multiply the second term by -1-1

Multiply the numerator and denominator of the second term by $-1$.

$\frac{10v}{2v-1}+\frac{2v+4}{1-2v}=\frac{10v}{2v-1}+\frac{-2v-4}{2v-1}$

Step 3. Add the numerators

Step 3. Subtract the Numerators

• As the denominator is same for both the terms, add the numerator and place over the common denominator.
• Add the like terms of the numerator.

$\begin{array}{rcl}\frac{10v}{2v-1}+\frac{-2v-4}{2v-1}& =& \frac{10v-2v-4}{2v-1}\\ & =& \frac{8v-4}{2v-1}\end{array}$

Step 4. Simplify

• Factor the expression in the numerator and then cancel out the common terms in numerator and denominator.

$\begin{array}{rcl}\frac{8v-4}{2v-1}& =& \frac{4\cancel{\left(2v-1\right)}}{\cancel{2v-1}}\\ & =& 4\end{array}$

• The sum is 4.